Aiming to describe traffic flow on road networks with long-range driver interactions, we study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable but also on the distribution of the population. We prove existence, uniqueness and continuous dependence results of the solution intended in a suitable measure-theoretic sense. We also provide a representation formula in terms of the push-forward of the initial and boundary data along the network and discuss an explicit example of nonlocal velocity field fitting our framework.

Measure-valued solutions to nonlocal transport equations on networks / Camilli, Fabio; DE MAIO, Raul; Tosin, Andrea. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 264:12(2018), pp. 7213-7241. [10.1016/j.jde.2018.02.015]

Measure-valued solutions to nonlocal transport equations on networks

Fabio Camilli
;
DE MAIO, RAUL
;
Andrea Tosin
2018

Abstract

Aiming to describe traffic flow on road networks with long-range driver interactions, we study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable but also on the distribution of the population. We prove existence, uniqueness and continuous dependence results of the solution intended in a suitable measure-theoretic sense. We also provide a representation formula in terms of the push-forward of the initial and boundary data along the network and discuss an explicit example of nonlocal velocity field fitting our framework.
Network, transport equation, measure valued solution
01 Pubblicazione su rivista::01a Articolo in rivista
Measure-valued solutions to nonlocal transport equations on networks / Camilli, Fabio; DE MAIO, Raul; Tosin, Andrea. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 264:12(2018), pp. 7213-7241. [10.1016/j.jde.2018.02.015]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1069014
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